Merton Structural Credit Distance-to-Default (DD) Formula

Measure how many asset-volatility sigmas separate a borrower from insolvency!

In Merton’s (1974) structural credit risk model, equity is a European call option on firm asset value V_A struck at the default point D (typically short-term liabilities plus half of long-term debt). Under geometric Brownian motion with expected asset drift mu_A and asset volatility sigma_A over horizon T years, log asset value at maturity has mean ln(V_A) + (mu_A - 0.5 * sigma_A^2) * T and standard deviation sigma_A * SQRT(T).

Therefore, exact Distance-to-Default DD = (LN(V_A / D) + (mu_A - 0.5 * sigma_A^2) * T) / (sigma_A * SQRT(T)) measures how many standard deviations firm assets can fall before breaching D! Even two firms with identical 33.3% asset cushion (1 - D / V_A) have dramatically different solvency risk if one carries sigma_A = 15% vs sigma_A = 40%.

Merton Physical Distance-to-Default (DD in Standard Deviations)

Computes exact Merton DD from market asset value B2, default barrier B3, asset drift B4, asset volatility B5, and horizon B6.

=IF(OR(B2 <= 0, B3 <= 0, B5 <= 0, B6 <= 0), "Invalid Credit Inputs", ROUND((LN(B2 / B3) + (B4 - 0.5 * (B5 ^ 2)) * B6) / (B5 * SQRT(B6)), 4))

Static Solvency Asset Cushion Ratio (1 - D / V_A)

Measures unscaled percentage asset buffer above default point D for comparison against volatility-adjusted DD.

=IF(B2 <= 0, 0, ROUND(1 - (B3 / B2), 4))

Further reading

• Merton, R. C. (1974) — On the Pricing of Corporate Debt: The Risk Structure of Interest Rates